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Question

If secθ+tanθ=x then find tan θ.

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Solution

secθ+tanθ=x(1)

Now, we know that

sec2θtan2θ=1

(sec2θtan2θ)(secθ+tanθ)=1

(secθtanθ)x=1

secθtanθ=1x(2)

Subtracting, (1)(2), we get

2tanθ=x1x

tanθ=12(x1x)

tanθ=12x(x21)

Hence, the answer is 12x(x21).

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